MULTI-MATERIAL TOPOLOGY OPTIMIZATION OF STRUCTURES BY USING THE METHOD OF MOVING ASYMPTOTES

This study aims to deal with multi-material topology optimization problems by using the Methods of Moving Asymptotes (MMA) method. The optimization problem is to minimize the strain energy while a certain amount of material is used. Several types of structures, including plane, plate and shell structures, are considered and optimal materials distribution is investigated. To parametrize the topology optimization problem, the Solid Isotropic Material with Penalization (SIMP) method is utilized. Analytical sensitivity analysis is performed to obtain the derivatives of the objective function and volume constraints with respect to the design variables. Two types of material with different modulus of elasticities are considered and, therefore, each element has two design variables. The first design variable represents the presence or absence of material in an element, while the second design variable determines the type of material assigned to the element. In order to analyze the structures required during the optimization process, the ABAQUS software is employed. To integrate the topology optimization procedure with ABAQUS model, a Python script is developed. The obtained results demonstrate the performance of the proposed method in generating reasonable and effective topologies.

Keywords:

Multi-material topology optimization , SIMP , Method of moving asymptotes , Strain energy minimization , plates , Shell structures